Question

If the relation R on the set X={1,2,3……7}defined by aRb iff a≡b(mod 3).Find the pairs in R,find the partition induced by the equivalence relation R on X.

Answer 1

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If the relation R on the set X={1,2,3……7}

aRb iff a≡b(mod 3)

So aRb iff 3 divides (a-b)

So

R = { (1,1),(1,4),(1,7),(2,2),(2,5),(3,3),(3,6),(4,1),(4,4),(4,7),(5,2),(5,5),(6,3),(6,6),(7,1),(7,4),(7,7) }

Hence the required partitions are

Cl(1)= {1,4,7} = Cl(4) = Cl(7)

Cl(2)= {2,5} = Cl(5)

Cl(3)= {3,6} = Cl(6)

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